This invention relates to multipliers and more particularly analog multipliers.
Analog multipliers are well known in the art. No so well known is the fact that analog multipliers operate on the so-called "translinear" principle. Barrie Gilbert, Current-mode Circuits From a Translinear Viewpoint, in CURRENT-MODE ANALOG INTEGRATED CIRCUIT DESIGN 11-91, (C. Toumazou et al. eds. 1990), incorporated herein by reference. The principle of translinearity states that, for a closed loop of PN junctions, the product of the current-densities in the clockwise direction is equal to the product densities in the counter-clockwise direction. For a loop of transistors having equal junction (emitter) areas, this relationship extends to the currents through the PN junctions as well.
FIG. 1 shows an example of a prior art analog multiplier 10. The multiplier 10 includes three input transistors Q1-Q3 and an output transistor Q4. In the multiplier 10, a relationship between the output current I.sub.G and the input currents I.sub.1, I.sub.2, and I.sub.3 can be derived using the translinear principle where the clockwise loop includes the base-to-emitter junctions of transistors Q3 and Q4 and the counter-clockwise loop includes the base-to-emitter junctions of transistors Q1 and Q2. For the case where the emitter areas of Q1-Q4 are equal, the currents I.sub.1, I.sub.2, I.sub.3, and I.sub.G can then be expressed by the following relationship: EQU I.sub.1 I.sub.2 =I.sub.3 I.sub.G, (1)
Rearranging the above relationship produces the following classical expression for the multiplier output current I.sub.G : EQU I.sub.G =I.sub.1 .times.I.sub.2 /I.sub.3. (2)
From equation 2 it is seen that the output current I.sub.G is proportional to the input currents I.sub.1, I.sub.2 and inversely proportional to the current I.sub.3.
The expression assumes that the input currents I.sub.1, I.sub.2, I.sub.3 are exactly replicated in the emitters of the corresponding transistors. Operational amplifiers (op-amps) 12, 14 and 16 are connected between the collector and the emitter of an associated transistor to "force" the collector currents in the associated transistors to be equal to the input currents I.sub.1, I.sub.2, I.sub.3. (See Gilbert, CURRENT-MODE ANALOG INTEGRATED CIRCUIT DESIGN at 37.) The op-amps force the collector currents equal to the input currents even for low values of current-gain, beta (.beta.=I.sub.C /I.sub.B). The op-amps thus provide added robustness to the analog multiplier across semiconductor process variations.
A problem with this design is that the operational amplifiers add significant complexity to the four transistor analog multiplier 10. Accordingly, a need remains a simple, yet robust, analog multiplier circuit.